Let I be a closed interval of the form [a, b], where a and b are real numbers and a ≤ b. We define the length of I as l(I):=b-a. Consider two closed intervals I₁, I₂. Show that (1₁) = (1₂) if and only if there exists y R such that 1₂ = (x+y: for some r € 1₁}. Hint: A sketch might be very helpful.

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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I used desmos to help but still cannot find the interval. Please explain it please. Thank you!

Let I be a closed interval of the form [a, b], where a and b are real numbers and a ≤ b. We define the
length of I as
l(I):=b-a.
Consider two closed intervals I₁, I₂. Show that (1₁) = (1₂) if and only if there exists y € R such that
1₂ = {2+y: for some 2 € I₁}.
Hint: A sketch might be very helpful.
Transcribed Image Text:Let I be a closed interval of the form [a, b], where a and b are real numbers and a ≤ b. We define the length of I as l(I):=b-a. Consider two closed intervals I₁, I₂. Show that (1₁) = (1₂) if and only if there exists y € R such that 1₂ = {2+y: for some 2 € I₁}. Hint: A sketch might be very helpful.
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